This work aims at developing a novel direct design and analysis method of learning control protocol toward consensus performance of multiagent systems (MASs) without using any model. A nonlinear autoregressive moving average (NARMA) function is designed at first to formulate the inherent consensus dynamics with respect to the consensus error and the control protocols. Then, a consensus performance-related iterative linear data model (CPiLDM) is constructed for equivalently reformulating the NARMA consensus system's iterative dynamics in a data-driven framework. The CPiLDM does not rely on a model no matter through first-principle modeling or system identification methods. Next, a direct distributed iterative learning control (DirDILC) method is developed through an optimization technique subject to the CPiLDM. The convergence is proved directly for the virtual NARMA consensus system, without relying on the dynamics of the agent itself, and thus simplifies the analysis consequently. Since the presented DirDILC is purely data-driven without relying on an explicit model, it constitutes a significant step forward from the existing consensus control theory.

This work investigates the consensus learning control for heterogeneous nonlinear multiagent systems (MASs) under false data injection (FDI) attacks on the communication channels. An enhanced iterative dynamic linearization (EiDL) method is introduced to transform the nonlinear MAS into an equivalent linearization data model, where additional parameters are used to reflect the uncertainties of the MAS. Assume that the communication among agents is subject to a stochastic FDI attack which is modeled by a weighted sum of attacks for adjacent communication channels. Then, combining the event-triggering condition along the iterative direction, an event-triggered data-driven iterative learning control (ET-DDILC) is proposed where the attacked information is used in control law and parameter estimation law to counteract the impact of FDI attacks. The convergence is proven by introducing additional tools of mathematical expectations and matrix theory. Moreover, the proposed ET-DDILC is further extended to the MASs under iteration-switching topologies. Extensive simulation results verify that the proposed ET-DDILC can achieve a good control performance against injection attacks without using any model information while simultaneously saving system resources through the event-triggering mechanism.

Considering the four challenges of non-identical initial states, non-repetitive uncertainties, different batch lengths, and unavailable mathematical model of a rubber mixing process (RMP), this article proposes a data-driven iterative learning temperature control (DDILTC) for the RMP. Specifically, an iterative linear data model (iLDM) is developed to formulate the iterative dynamics of RMP and is further used as a one-step iterative linear predictive model to estimate the RMP’s temperature that is unavailable when the current batch length is shorter than the desired one. The unknown parameters of the iLDM are estimated iteratively by designing an iterative adaption law. Further, an iterative learning based observer is designed to estimate the non-repetitive uncertainties and non-identical initial states as an extended state. The proposed DDILTC is a data-driven method and the iLDM is only used to formulate the iterative relationship of the input-output between two batches instead of a mathematical model of the RMP with physical meanings. Simulation study verifies the results. Note to Practitioners—The mixing temperature of a rubber mixing process (RMP) is a critical variable, ensuring the desired plasticity and viscosity of the rubber compounds. Indeed, RMP is a typical batch process performing repetitively over the finite time interval. However, no ILC results about the RMP temperature control have been reported even though ILC can learn the control experience from the past batches to improve control performance. The main reason lies in that the practical environments of RMP make it impossible to satisfy the strictly repetitive conditions, i.e., the initial states, disturbances, and batch lengths are all iteration-varying. Furthermore, it is difficult to establish a mathematical model of the RMP due to its large production scale and complex dynamics along both time and iteration directions. Therefore, the main motivation of this paper is to study the iterative learning temperature control problem of RMP by considering the nonrepetitive uncertainties of initial states, disturbances, and batch lengths, bypassing the use of any model information. An iterative linear data model (iLDM) is established to equivalently reformulate the unavailable two-dimensional dynamic behavior of RMP and to facilitate the controller design and analysis. The gradient uncertainty of RMP is reformulated as the unknown parameters in the iLDM and can be iteratively estimated by designing an iterative adaptation algorithm. The non-repetitive initial states and disturbances can be estimated by designing an iterative observer. Moreover, the unavailable mixing temperatures at the unreachable operation points are estimated by using the iLDM as the iterative predictive model. To summarize, the proposed method is simple in computation and easy in implementation since only the I/O data is used, and thus it is of great practical significance.

Aiming to solve issues of limited resources in topology network communication, unavailability of the mathematical models, direct controller design without considering system dynamical formulation, and lack of efficient use of learning ability from repetitive operations, an event-triggered direct data driven iterative learning control (ET-DirDDILC) is developed for a multiagent system (MAS). Since the control protocol directly affects control performance, there is definitely a close relationship between the consensus performance of the agents and the control protocols. To this end, a nonaffine nonlinear relationship of consensus error regarding the control protocol is established. Then, to deal with the unknown nonlinearity, a dynamic linear input–output relationship between two triggered batches is established by an event-triggering linearly parametric data model (ET-LPDM) where a triggering mechanism is designed along the iteration axis. Furthermore, both the event-triggered control law and the event-triggered parameter estimation law are derived from two objective functions, respectively, by using the ET-LPDM, where the values at nontriggering iteration remain unchanged from the latest triggering iteration to reduce the consumption of system resources. The proposed ET-DirDDILC does not rely on the MAS dynamical formulation. The convergence is proved and simulation study verifies the effectiveness of the presented ET-DirDDILC for MASs with both fixed and switching topologies.

This work aims at presenting a new sampled-data model-free adaptive control (SDMFAC) for continuous-time systems with the explicit use of sampling period and past input and output (I/O) data to enhance control performance. A sampled-data-based dynamical linearization model (SDDLM) is established to address the unknown nonlinearities and nonaffine structure of the continuous-time system, which all the complex uncertainties are compressed into a parameter gradient vector that is further estimated by designing a parameter updating law. By virtue of the SDDLM, we propose a new SDMFAC that not only can use both additional control information and sampling period information to improve control performance but also can restrain uncertainties by including a parameter adaptation mechanism. The proposed SDMFAC is data-driven and thus overcomes the problems caused by model-dependence as in the traditional control design methods. The simulation study is performed to demonstrate the validity of the results.

In this work, a data-driven indirect iterative learning control (DD-iILC) is presented for a repetitive nonlinear system by taking a proportional-integral-derivative (PID) feedback control in the inner loop. A linear parametric iterative tuning algorithm for the set-point is developed from an ideal nonlinear learning function that exists in theory by utilizing an iterative dynamic linearization (IDL) technique. Then, an adaptive iterative updating strategy of the parameter in the linear parametric set-point iterative tuning law is presented by optimizing an objective function for the controlled system. Since the system considered is nonlinear and nonaffine with no available model information, the IDL technique is also used along with a strategy similar to the parameter adaptive iterative learning law. Finally, the entire DD-iILC scheme is completed by incorporating the local PID controller. The convergence is proved by applying contraction mapping and mathematical induction. The theoretical results are verified by simulations on a numerical example and a permanent magnet linear motor example.

This article develops a novel data-driven finite-iteration learning control (DDFILC) for the nonlinear repetitive systems that are stable for the finite operation length. Both the error range and the finite-iteration number can be designated beforehand by considering the efficiency and economy of the industrial processes. As a result, not only can the proposed DDFILC guarantee the desired product quality but also can reduce the operation cost. First, a linear data model (LDM) is constructed to reformulate the system dynamics that satisfies the Lipschitz continuity condition. Then, an iterative updating law of the DDFILC is developed for estimating the unknown parameter of the LDM. The proportional-differential type learning law used in the DDFILC has two iteration-time-varying learning gains, both of which are updated according to the linear matrix inequality conditions. Not only the finite-iteration convergence but also the iteratively asymptotic convergence can be shown mathematically by using the two-dimensional (2-D) system theory. The proposed DDFILC approach does not require an exact model and is robust to uncertainties. The simulation study verifies the results.

This work aims at improving the control performance of the iterative learning control through set-point learning along iteration direction. A double-layered learning control mechanism is designed for both the control input and the set-point, respectively. The learning control of the input is regarded as a local controller in the inner layer, and the learning control of the set-point is designed as an auxiliary controller in the outer layer whose design is a main challenge since no any priori knowledge is available to describe the relationship between the set-point and the control performance. To solve this issue, an ideal nonlinear nonaffine set-point learning optimization (SPLO) algorithm is designed by taking the set-point and the tracking error as the arguments. Then, an iterative dynamic linearization (iDL) is introduced to formulate the ideal SPLO algorithm as a linear parametric one whose unknown parameter is estimated by designing a parameter updating algorithm. Further, since a strongly nonlinear and nonaffine system is considered without any model information available, the iDL is also used to derive its equivalent linear data model which is then updated by the input and output data to make the linear parametric SPLO realizable. Finally, a double-layered iterative learning control (DLILC) is proposed under the data-driven framework for tracking an iteration-varying trajectory. Convergence analysis and extensive simulations are included to demonstrate the effectiveness of the presented DLILC.

This article aims at solving the problems of data-driven control design in the presence of strong uncertainties, hard nonlinearities, and model dependency by using a dynamic linearization (DL) method and an extended state observer (ESO). An unknown nonlinear nonaffine system is considered, whose input–output dynamics is then equivalently reformulated into a modified linear data model (mLDM) in which both a linear parametric increment description that is affine to the control input and the unmodeled uncertainties along with disturbances are included without omission or approximation. The uncertain parameter of the mLDM is estimated in real time by designing an adaptive mechanism, and the unmodeled uncertainties and disturbances are considered as a total extended state which is further estimated by developing a linear ESO. Subsequently, a modified DL-and-ESO-based data-driven adaptive control (mDLESO-DDAC) is proposed by using knowledge from previous control input to improve the control performance. The theoretical results are mathematically proved and then verified by simulations.

In this work, a data-driven virtual reference setting learning (DDVRSL) method is proposed to enhance the proportional-derivative (PD) feedback controller of the repetitive nonlinear system. First, an ideal nonlinear virtual reference setting learning law is presented in the outer loop of the control system to tune the reference setting. Such an ideal nonlinear learning law exists theoretically and is transferred to a linear parametric DDVRSL via iterative dynamic linearization (IDL). Next, an iterative adaptation law is proposed for the estimation of the parameters in the DDVRSL law subject to the nonlinear system which is also transferred into a linear form by using the IDL method. The iterative adaptation algorithm tunes the learning gains of DDVRSL law using input and output measurements, therefore improving the robust ability against uncertainties. The proposed DDVRSL-based PD control method does not require any exact mechanistic model knowledge. The convergence is proved via the contraction mapping principle, mathematical induction, and time-weighted norm. Further, the theoretical results are verified through simulations.

In this article, the optimal consensus problem at specified data points is considered for heterogeneous networked agents with iteration-switching topologies. A point-to-point linear data model (PTP-LDM) is proposed for heterogeneous agents to establish an iterative input-output relationship of the agents at the specified data points between two consecutive iterations. The proposed PTP-LDM is only used to facilitate the subsequent controller design and analysis. In the sequel, an iterative identification algorithm is presented to estimate the unknown parameters in the PTP-LDM. Next, an event-triggered point-to-point iterative learning control (ET-PTPILC) is proposed to achieve an optimal consensus of heterogeneous networked agents with switching topology. A Lyapunov function is designed to attain the event-triggering condition where only the control information at the specified data points is available. The controller is updated in a batch wise only when the event-triggering condition is satisfied, thus saving significant communication resources and reducing the number of the actuator updates. The convergence is proved mathematically. In addition, the results are also extended from linear discrete-time systems to nonlinear nonaffine discrete-time systems. The validity of the presented ET-PTPILC method is demonstrated through simulation studies.

An event-triggered nonlinear iterative learning control (ET-NILC) method is presented for repetitive nonaffine and nonlinear systems that have 2-D dynamic behavior along both time and iteration directions. Based on the virtual linear data model, the ET-NILC method is proposed by designing an event triggering condition based on the Lyapunov-like stability analysis conducted along the iteration direction. The learning gain function of ET-NILC is nonlinear and updated by designing an iterative learning parameter estimation law to enhance the robustness. From the perspective of the time dynamics, the proposed ET-NILC is a feedforward control and the event-triggering condition can be verified offline using tracking errors, event triggering errors, and the estimated parameters together. Moreover, the proposed ET-NILC is a data-driven scheme since it merely uses I/O data for the design. The results are also extended to repetitive multiple-input-multiple-output (MIMO) nonaffine nonlinear systems using the property of input-to-state stability as the basic mathematical tool. The convergence of the proposed ET-NILC methods is proved. Several simulations illustrate the effectiveness of the proposed methods.

This paper investigates an event-triggered model-free adaptive control for nonaffined nonlinear systems under a data-driven design framework. By introducing a compact form dynamic linearization (CFDL) scheme, a linear data model of the nonlinear nonaffine system is derived. Then, a parameter estimation algorithm is developed to offline identify the linear data model. On the basis of the identified linear data model, a CFDL-based event-triggered model-free adaptive control (CFDL-ET-MFAC) is developed by designing an event-triggering condition to guarantee the Lyapunov stability. The control action is active only when the event-triggering condition is satisfied. Otherwise, the input signal remains the same as that at the previous triggering instant. In addition, the parameter estimation algorithm is developed for the proposed CFDL-ET-MFAC to identify the CFDL model in real time for improving the robustness to the uncertainties. Meanwhile, both a partial form dynamic linearization-based event-triggered MFAC and a full form dynamic linearization-based event-triggered MFAC are proposed to further improve the control performance by using additional parameters to capture the more complicated behavior of complex nonlinear systems. The proposed ET-MFAC methods only rely on the linear data models directly obtained from data without using any other mechanistic model information. The validity of the three ET-MFAC methods is confirmed through both theoretical analysis and simulation studies.

This paper reconsiders the iterative learning control (ILC) problem for variable trial lengths via compensating output data by using an auxiliary predictive model when the controlled process does not reach the desired trial length. Moreover, this paper aims to propose a general and data-driven ILC method without requiring any explicit mechanistic model information. Specifically, an iterative difference with state transition expression is performed at first over the desired trial length in iteration domain to build an auxiliary predictive model for the iterative input-output dynamics of the linear discrete-time system. Then, an auxiliary predictive compensation-based ILC (APC-ILC) method is presented by defining an expanded output variable in which the predictive output is incorporated to compensate the unavailable output data due to the shorter operation length. The learning gain is iteration-time-varying and is updated using real-time data to adapt to system changes. Furthermore, the proposed learning control law contains additional input information to further improve the control performance. Theoretical analysis and simulations further verify the effectiveness of the proposed APC-ILC.

In this paper, a new data-driven ILC method is proposed for I/O constrained nonlinear systems. An iterative dynamic linearization is introduced for the controlled nonlinear systems. All of the constraints on the system inputs and outputs are reformulated with a linear matrix inequality. The learning control law is then developed by minimizing a predesigned cost function subjected to the linear matrix inequality constraint. Simulation results illustrate the effectiveness of the proposed approach.